1. Problem: Solve the system of equations using substitution and elimination methods. Given: $$\begin{cases} x + y = 10 \\ x - y = 2 \end{cases}$$ 2. Using substitution: From the first equation, express $x$ in terms of $y$: $$x = 10 - y$$ 3. Substitute $x = 10 - y$ into the second equation: $$ (10 - y) - y = 2 $$ 4. Simplify: $$ 10 - y - y = 2 $$ $$ 10 - 2y = 2 $$ 5. Solve for $y$: $$ 10 - 2y = 2 $$ $$ -2y = 2 - 10 $$ $$ -2y = -8 $$ $$ y = \frac{-8}{\cancel{-2}} \cancel{-1} = 4 $$ 6. Substitute $y = 4$ back into $x = 10 - y$: $$ x = 10 - 4 = 6 $$ 7. Final answer: $$ x = 6, \quad y = 4 $$